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The method is based on the result that any LAP solution of a halfguide problem can be extended to the LAP solution of a fullguide problem. At the end of this paper, we also give some numerical results to show the efficiency of our numerical methods.<\/jats:p>","DOI":"10.1007\/s00211-021-01229-0","type":"journal-article","created":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T17:04:37Z","timestamp":1629133477000},"page":"959-996","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Numerical methods for scattering problems in periodic waveguides"],"prefix":"10.1007","volume":"148","author":[{"given":"Ruming","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,16]]},"reference":[{"issue":"3","key":"1229_CR1","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1137\/100791798","volume":"71","author":"V Hoang","year":"2011","unstructured":"Hoang, V.: The limiting absorption principle for a periodic semin-infinite waveguide. 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